The adhesive interactions between cells and surfaces play a key role in many vital physiological processes, such as the innate immune response or wound healing, but also in targeted drug delivery and active control on the adhesion of viruses.
Adhesion is often mediated by specific intermolecular bonds, which generally function under considerable mechanical load. Bond properties can be explored by dynamic force spectroscopy, which measures the force required to separate two surfaces connected by small numbers of molecular bonds. Motivated by such experiments, the aim of this thesis is to investigate the adhesive effects of discrete, stochastic binding of clusters of intermolecular bonds, supported by a rigid or flexible substrate.
The stochastic adhesion of a cluster of bonds connecting a rigid disk and a flat surface is investigated within the framework of piecewise deterministic Markov processes. The model accounts for the rupture and rebinding of discrete bonds, depending on the disk’s motion under applied force. Hydrodynamic forces in the thin layer of viscous fluid between the two surfaces are described using lubrication theory. Bonds are modeled as identical, parallel springs, and equally share the load. Monte Carlo simulations, capturing the stochastic evolution of clusters with few bonds are complemented by various deterministic approximations. Dynamic force spectroscopy experiments are mimicked under linearly ramped force.
The stochastic evolution of a bond population connecting a flexible membrane to a rigid wall within a fluid is also formulated as a Markov process, and spatial effects are considered by allowing the vertical elastic bonds to differentially share the load, depending on their extension. The deterministic motion of the membrane, interrupted by stochastic binding and unbinding of bonds, is formulated as a partial differential equation, derived using lubrication theory. The average population and extension of bonds are shown to be inversely correlated, using a wavelet-based semblance method.